The Proper Test Index

Introduction

In No Laying Up’s coverage of the 125th U.S. Open at Oakmont, the Big Man himself introduced a metric that has lodged itself in my brain: the Proper Test Index (PTI). It’s defined as

\[ PTI = \frac{\text{Number of rounds with a score >= 80}}{\text{Number of rounds with a score of < 70}} \]

He ran through some of the numbers across past U.S. Opens, but what does it look like when we extend the metric to the PGA Tour? Using Data Golf’s API, I pulled the scoring data for their entire archive and calculated the event-level PTI:

A few things stood out to me.

• The pros are really good. Across the entire dataset, only 1.0% of rounds have a score of 80 or over. That’s compared to a healthy 37.2% of rounds falling in the 60s (or lower!).
• There are 140 events that had 0 rounds of 80 or over.
• What were we doing at the 2019 Wyndham Championship? 332 rounds below 70 and 0 above 80. Not Proper.

Now when it comes to majors…

As much as I like Brooks Koepka…, the 2018 PGA Championship at Bellerive CC wasn’t particularly proper. But good news for Big! Phil the Thrill’s unbelievable performance in the 2021 PGA Championship at Ocean Course at Kiawah Island was undeniable. Proper.

Sabermetrics can help us identify Proper Venues

PTI tells us something about the balance of extreme rounds at the event level. What if we adopt Baseball’s park factor to figure out if a low round really matters?

\[ \text{Course Factor} = \frac{\frac{\text{Total scores >= 80 at the course}}{\text{Total scores < 70 at the course}}}{\frac{\text{Total scores >= 80 at all other courses}}{\text{Total scores < 70 at all other courses}}} \]

The larger the course factor, the more impressive a 65 is! Let’s plot out the course factor across the available venues.

Wow. Course Factor has some range! According to this metric, An above average round at Ocean Course at Kiawah Island is worth 1954 times more than a similarly above average round at Sea Island GC (Seaside). Remember what we’re talking about rare events here; so if 8.3% of rounds at Ocean Course at Kiawah Island are over 80 (and only 6.4% below 70), we will see some extreme values.

A logarithmic scale gives us a bit more insight into how the course factor relates to pure scoring average.

This chart is more legible. Due to the strict scarcity of rounds in the 80s, we’ll be using a logarithmic transformation of course factor (\(\text{Course Factor}^{*}\)) to convey the relative difficulty of each venue.

Now comes the real question, however: Did Big Cook?

Looking at the distribution of scores across each venue,

I think Big might have cooked here! \(\text{Course Factor}^{*}\) seems to correlate not only with average difficulty, but variance. In a proper test, we want to see separation between the “Men” and the “Little Boys”.

Can measuring venue difficulty help us understand player performance?

Ok, enough about venues. How do we convert this into a measure of player performance? Simple, a weighted average of a player’s score against the wave average (where tee times are available).

\[ \text{Proper Player Index} = \frac{\sum (\text{Wave Scoring Average} - \text{Score}) \times \log_{10}(1 + \text{Course Factor})}{\sum \text{Course Factor}} \]

The interesting comparison here is with Strokes Gained (Total). In theory, these metrics operate on the same scale, right? The only thing we’ve done is weight the Proper rounds. I’m proposing 4 different categories: